Homology, Homotopy and Applications Volume 4 (2002), No. 2

Special issue in honor of Jan Erik Roos on the occasion of his 65th birthday

Editor Larry Lambe Guest Editor Clas Löfwall Table of Contents

1. The work of Jan-Erik Roos on the cohomology of commutative rings Luchezar L. Avramov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–16

2. Homotopy Lie algebras and Poincaré series of algebras with monomial relations Luchezar L. Avramov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17–27

3. Secondary cohomology and the Steenrod square Hans–Joachim Baues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29–62

4. Crossed extensions of algebras and Hochschild cohomology Hans-Joachim Baues and Elias Gabriel Minian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63–82

5. An analogue of holonomic D-modules on smooth varieties in positive characteristics Rikard Bögvad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83–116

6. An algebraic model for homotopy fibers Nicolas Dupont and Kathryn Hess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117–139

7. Nonsplit extensions of modular Lie algebras of rank 2 A. S. Dzhumadil’daev and S. S. Ibraev . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141–163

8. Trees, Free Right-Symmetric Algebras, Free Novikov Algebras and Identities Askar Dzhumadil’daev and Clas Löfwall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165–190

9. On minimal models in integral homotopy theory Torsten Ekedahl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191–218

10. Growth and Lie brackets in the homotopy Lie algebra Yves Félix, Stephen Halperin and Jean-Claude Thomas . . . . . . . . . . . . . . . . . . . . . 219–225

11. Koszul homology and Lie algebras with application to generic forms and points R. Fröberg and C. Löfwal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227–258

12. Defining relations for classical Lie superalgebras without Cartan matrices P. Grozman, D. Leites and E. Poletaeva . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259–275

13. Resolutions by mapping cones Jürgen Herzog and Yukihide Takayama . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277–294

14. Presentation Depth and the Lipman-Sathaye Jacobian Theorem Melvin Hochster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295–314

15. On Constructing Resolutions Over the Polynomial Algebra Leif Johansson, Larry Lambe and Emil Sköldberg . . . . . . . . . . . . . . . . . . . . . . . . . . . 315–336

16. A periodisation of semisimple Lie algebras Anna Larsson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337–355 17. Noncommutative deformations of modules

O. A. Laudal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357–396

18. The Riemann tensor for nonholonomic manifolds Dimitry Leites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397–407

19. Some conjectures about the Hilbert series of generic ideals in the exterior algebra Guillermo Moreno-Socías and Jan Snellman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409–426

20. Resolutions and Lattices Irena Peeva . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427–437

Homology, Homotopy and Applications (ISSN 1512 - 0139) is the all-electronic, refereed journal on Homological and Homotopical Algebra and their applications in the mathematical sciences.

The influence of homology and homotopy is found in many fundamental domains of mathematics and the aim of “Homology, Homotopy and Applications” is to unify such applications, to show its merit, importance and diversity and to present in time to its reader new information about the progress of the area and the relationships with other fields.

To this end “Homology, Homotopy and Applications” will publish carefully refereed significant and original research papers and expository survey papers of high level in the area, as well as research papers having substantial applications of results and technique of homological and homotopical algebra, for example to general algebra, algebraic topology, algebraic homotopy, algebraic geometry, K-theory, category theory,computer science, Galois theory, functional analysis, algebraic number theory, differential geometry and topology.

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EDITORIAL BOARD

Editors-in-Chief:

Hvedri Inassaridze, A. Razmadze Mathematical Institute, Georgian Academy of Sciences, M. Alexidze Str.1, Tbilisi 380093, Georgia.

hvedri@rmi.acnet.ge    hvedri.inassari@usa.net

Gunnar Carlsson, University of Stanford, USA

gunnar@math.stanford.edu

Managing Editors:

Ronald Brown, University of North Wales, UK: r.brown@bangor.ac.uk J. Nigel Ray, University of Manchester, UK: nige@ma.man.ac.uk Lionel Schwartz, Universit de Paris 13, France: schwartz@math.univ-paris13.fr

Editors:

Luchezar Avramov, Purdue University, USA:

    avramov@Math.Purdue.Edu

Michael Barr, McGill University, Canada:

    barr@triples.math.mcgill.ca

Lawrence Breen, Universite de Paris 13, France:

    breen@math.univ-paris13.fr

Winfried Bruns, Universitt Osnabrck, Germany:

    winfried@mathematik.Uni-Osnabrueck.de

Aurelio Carboni, University of Insubria, Italy:

    acarboni@mailserver.unimi.it

Antonio Martinez Cegarra, University of Granada, Spain:

    acegarra@goliat.ugr.es

Claude Cibils, University of Montpellier, France.

    cibils@math.univ-montp2.fr

Ralph Cohen, Stanford University, USA:

    ralph@math.stanford.edu

R. Keith Dennis, Cornell University, Ithaca, USA:

    rkd@ams.org,
    dennis@math.cornell.edu

Graham Ellis, University College of Galway, Ireland:

    Graham.Ellis@ucg.ie

Daniel Guin, University of Montpellier, France

    dguin@math.univ-montp2.fr

Jürgen Herzog, Universität GH Essen, Germany:

    mat300@uni-essen.de

Johannes Hübschmann, Université de Lille, France:

    Huebschmann@Univ-Lille1.fr

G. Max Kelly, University of Sydney, Australia:

    maxk@maths.usyd.edu.au

Frans Keune, University of Nijmegen, The Netherlands:

keune@sci.kun.nl

Larry Lambe, University of Stockholm, Sweden:

lambe@matematik.su.se

Jean-Louis Loday, Universit de Strasbourg, France:

loday@math.u-strasbg.fr

Andy R. Magid, University of Oklahoma, USA:

amagid@uoknor.edu

Wolfgang Metzler, University of Frankfurt, Germany

metzler@math.uni-frankfurt.de

R. James Milgram, Stanford University, USA:

milgram@math.stanford.edu

Alexander Mishchenko, Moscow State University, Russia

asmish@mech.math.msu.su

Shigeyuki Morita, University of Tokyo, Japan:

morita@ms.u-tokyo.ac.jp

Maria Cristina Pedicchio, University of Trieste, Italy:

pedicchi@uts.univ.trieste.it

Ulf Rehmann, University of Bielefeld, Germany:

rehmann@mathematik.uni-bielefeld.de

Jonathan M. Rosenberg, University of Maryland, USA:

jmr@math.umd.edu

Andrea Solotar, University of Buenos Aires, Argentina

asolotar@dm.uba.ar,
asolotar@topo.math.u-psud.fr

James Stasheff, University of North Carolina, USA:

jds@math.unc.edu

Ross Street, Macquarie University, Australia:

street@macadam.mpce.mq.edu.au

Tomohide Terasoma, University of Tokyo, Japan:

terasoma@gauss.ms.u-tokyo.ac.jp

Walter Tholen, York University, Canada:

tholen@mathstat.yorku.ca

Charles A. Weibel, Rutgers University, New Brunswick, USA:

weibel@euler.rutgers.edu